In this work, the problem of optimization of low-thrust reconfiguration maneuvers for spacecraft flying in formation is addressed. The problem is stated as the solution of an optimal control problem in which an object...
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In this work, the problem of optimization of low-thrust reconfiguration maneuvers for spacecraft flying in formation is addressed. The problem is stated as the solution of an optimal control problem in which an objective function related to controls is minimized, satisfying a series of constraints on the trajectory that are both differential and algebraic. The problem has been faced by transcribing the differential constraints into a nonlinear programming problem with a parallel multiple-shooting method. The resulting problem has been solved with an interior point method. The method that has been developed is particularly suited for the solution of problems in which the trajectory is constrained with a great number of inequalities on both states and controls. The method has been applied to the design of reconfiguration maneuvers for spacecraft flying in formation;for which the collision avoidance issue leads to the imposition of a large number of inequalities on states derived from the minimum distance constraint.
A globally optimal Superconducting magnet coil design procedure based on the Minimum Stored Energy (MSE) Current density map is outlined. The method has the ability to arrange coils in a manner that generates a strong...
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A globally optimal Superconducting magnet coil design procedure based on the Minimum Stored Energy (MSE) Current density map is outlined. The method has the ability to arrange coils in a manner that generates a strong and homogeneous axial magnetic field over a predefined region, and ensures the stray field external to the assembly and peak magnetic field at the wires are in acceptable ranges. The outlined strategy of allocating coils within a given domain suggests that coils should be placed around the perimeter of the domain with adjacent coils possessing alternating winding directions for optimum performance. The underlying current density maps from which the coils themselves are derived are unique, and optimized to possess minimal stored energy. Therefore, the method produces magnet designs with the lowest possible overall stored energy. Optimal coil layouts are provided for unshielded and shielded short bore symmetric superconducting magnets. Crown Copyright (C) 2008 Published by Elsevier Inc. All rights reserved.
A new class of optimization problems is discussed in which some constraints must hold in certain regions of the corresponding space rather than everywhere. In particular, the optimal design of topologies for mechanica...
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A new class of optimization problems is discussed in which some constraints must hold in certain regions of the corresponding space rather than everywhere. In particular, the optimal design of topologies for mechanical structures can be reduced to problems of this kind. Problems in this class are difficult to analyze and solve numerically because their constraints are usually irregular. Some known first- and second-order necessary conditions for local optimality are refined for problems with vanishing constraints, and special Newton-type methods are developed for solving such problems.
THERE exist various strategies [1,2] for reaching numerical 1 solutions to the nonlinear optimal control problem. The directmultiple-shooting (DMS) method is usually preferred for analyzing general nonlinear optimal c...
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THERE exist various strategies [1,2] for reaching numerical 1 solutions to the nonlinear optimal control problem. The directmultiple-shooting (DMS) method is usually preferred for analyzing general nonlinear optimal control problems due to its convenience in handling system constraints and a large convergence radius compared with other methods. However, these advantages can be decreased in case the estimation of the related Karush-Kuhn-Tucker (KKT) system is not accurate enough to guarantee robust analyses. The related estimation errors are originated from time integration and finite difference approximation in the standard DMS method. The present work intends to propose a new method of accurately estimating the KKT system. For this purpose, the state-dependent coefficient (SDC) factorization method, which has been successfully implemented in the state-dependent Riccati equation (SDRE) technique [3-5], is used to derive a linear system structure from the nonlinear motion equation. Applying the linear system theory to the resultant SDC form of equations, the KKT system can be built without resorting to any time integration and finite difference formula to calculate of gradients and Hessian matrices, as opposed to the standard DMS method. The present paper proves that the convergence and the accuracy of the DMS method can be greatly enhanced through the applications of the new method to the rotorcraft trajectory tracking problem.
A well-known difficulty arising in the convergence globalization of Newton-type constrained optimization methods is the Maratos effect, which prevents these methods from achieving a superlinear convergence rate and, i...
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A well-known difficulty arising in the convergence globalization of Newton-type constrained optimization methods is the Maratos effect, which prevents these methods from achieving a superlinear convergence rate and, in many cases, reduces their general efficiency. For the sequential quadratic programming method with linesearch, a new simple and rather promising technique is proposed to avoid the Maratos effect.
Loading distribution for heavy plate mill is to find optimal control solutions under the granted performance indicators and constraints including mill capacity and hypothesis of rolling *** solutions are quite differe...
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Loading distribution for heavy plate mill is to find optimal control solutions under the granted performance indicators and constraints including mill capacity and hypothesis of rolling *** solutions are quite different for different performance *** the article,the performance indicators and sequential quadratic programming(SQP for short below) methods employed in 5 000 mm heavy plate mill of BaoSteel are penetratingly ***,the SQP method is an effective and fast way to solve the nonlinear programming problems with small or medium scale *** in 1976,Han put forward the SQP method for the first time and Powell made it perfect and accomplished the algorithm in *** fact, SQP method was to turn a nonlinear programming problem to a series of sub set of quadraticprogramming *** the algorithm,each iteration step is to solve one quadraticprogramming *** optimal solutions will be gradually approached after quadraticprogramming problems were totally *** solving the quadraticprogramming problem,the active set strategy were employed which turned the constrained quadraticprogramming problem to unconstrained quadraticprogramming *** active set strategy made the whole quadraticprogramming problem be solved by a least square *** finally, the matrix of the least square problem would be decomposed by Q matrix and R *** Q matrix and R matrix were obtained,the optimal solutions would be finally *** loading distribution,the performance indicators were composed by plate shape and draft of each *** shape is represented by rolling force gradually reduced pass by pass with a tunable *** mill capacity is another performance indicator represented by draft of each *** heavy plate mill,the mill capacity here is the motor moment. For heavy draft,the motor would be overloaded especially for the first several passes;for small draft,the motor would be loaded ***
Manipulation by juggling of an object by a 1-DoF prismatic arm is studied. The manipulation task is decomposed into two phases: accelerating phase and decelerating phas. The manipulation task is modeled as an optimiza...
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ISBN:
(纸本)9781424447749
Manipulation by juggling of an object by a 1-DoF prismatic arm is studied. The manipulation task is decomposed into two phases: accelerating phase and decelerating phas. The manipulation task is modeled as an optimization problem in order to get maximum flight while having minimum impact at catch time. The optimization problem is solved using sequential quadratic programming method and the results are verified by simulations in ADAMS.
Broadband data-independent beamforming designs aiming at constant beamwidth often lead to superdirective beamformers for low frequencies, if the sensor spacing is small relative to the wavelengths. Superdirective beam...
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ISBN:
(纸本)9781424423538
Broadband data-independent beamforming designs aiming at constant beamwidth often lead to superdirective beamformers for low frequencies, if the sensor spacing is small relative to the wavelengths. Superdirective beamformers are extremely sensitive to spatially white noise and to small errors in the array characteristics. These errors are nearly uncorrelated from sensor to sensor and affect the beamformer in a manner similar to spatially white noise. Hence the White Noise Gain (WNG) is a commonly used measure for the robustness of beamformer designs. In this paper, we present a method which incorporates a constraint for the WNG into a least-squares beamformer design and still leads to a convex optimization problem that can be solved directly, e.g. by sequential quadratic programming. The effectiveness of this method is demonstrated by design examples.
We introduce in this work a PDE-constrained approach to optical tomography that makes use of an all-at-once reduced Hessian sequential quadratic programming (rSQP) scheme. The proposed scheme treats the forward and in...
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ISBN:
(纸本)9780819474209
We introduce in this work a PDE-constrained approach to optical tomography that makes use of an all-at-once reduced Hessian sequential quadratic programming (rSQP) scheme. The proposed scheme treats the forward and inverse variables independently, which makes it possible to update the radiation intensities and the optical coefficients simultaneously by solving the forward and inverse problems, all at once. We evaluate the performance of the proposed scheme with numerical and experimental data, and find that the rSQP scheme can reduce the computation time by a factor of 10 to 25, as compared to the commonly employed limited memory BFGS method.
In order to solve error between the system output values and the model estimation values in non-linear system. A new method, the Particle Swarm Optimization & sequential quadratic programming (PSO-SQP), is propose...
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ISBN:
(纸本)9780769538921
In order to solve error between the system output values and the model estimation values in non-linear system. A new method, the Particle Swarm Optimization & sequential quadratic programming (PSO-SQP), is proposed to realize the on-line optimization to nonlinear complex system. Firstly, the PSO-SQP algorithm is proposed to solve the slow search speed of the PSO and easy convergence to the local minimum points of SQP. Then the method that the unknown parameters and states are estimated by the moving window based on Moving Horizon Estimation (MILE) is also described in the paper. Finally, the two examples are simulated to test those methods. It is validated that this method can cut down iteration times about 40%similar to 60%, the optimization of this algorithm can be about up to 30% on average.
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